This preview shows page 1. Sign up to view the full content.
Unformatted text preview: t
3 −1
2 + e2t
3 4
4 , 2 × 2 Exercise Set C (distinct roots), November
[6] Solve the di erential equation y = Ay where
−3 2
,
−3 2 A= λ = −1, 0 3 −2
3 −2 eAt = e−t y(0) = −2 2
−3 3 + 1
2 y = e−t −1
−1 + 2
2 + 2
3 [7] Solve the di erential equation y = Ay where
A= λ = −3, 0 eAt = e−3t
3 −2 −1
,
−2 −1 21
21 + 1
3 y ( 0) = 1 −1
−2
2 1
0 y= e−3t
3 1
3 [8] Solve the di erential equation y = Ay where
A= λ = 0, 1 eAt = −1 −2
,
1
2 2
2
−1 −1 + et y(0) = −1 −2
1
2 1
0 y= 2
−1 + et −1
1 1
−2 , 2 × 2 Exercise Set D (repeated roots), November 2 × 2 Exercise Set D (repeated roots)
Linear Algebra, Dave Bayer, November , [1] Find An where A is the matrix
A= λ = −2, −2 An = (−2)n 1
3
−3 −5
10
01 + n (−2)n−1 3
3
−3 −3 [2] Find An where A is the matrix
A= λ = 0, 0 A n = 0n 1
1
−1 −1
10
01 + n 0n−1 1
1
−1 −1 [3] Find An where A is the matrix
A= λ = 1, 1 An = 0 −1
1
2
10
01 +n −1 −1
1
1 [4] Find An where A is the matrix
A= λ = 4, 4 An = 4n 2 −1
4
6
10
01 + n 4n−1 −2 −1
4
2 [5] Find An where A is the matrix
A= λ = 1, 1 An = 6
5
−5 −4
10
01 [6] Find An where A is the matrix
A= 61
−1 4 +n 5
5
−5 −5 , 2 × 2 Exercise Set D (repeated roots), November λ = 5, 5 A n = 5n 10
01 + n 5n−1 1
1
−1 −1 [7] Find An where A is the matrix
A= λ = −1, −1 An = (−1)n 4 −5
5 −6
10
01 + n (−1)n−1 5 −5
5 −5 [8] Find An where A is the matrix
A= λ = −3, −3 An = (−3)...
View
Full
Document
 Spring '14
 DaveBayer
 Linear Algebra, Algebra

Click to edit the document details